In a perfect square, all the prime constituents have to be raised to an even number. For example, 16 is perfect square which is equal to 2 raised to the power 4. 81 is a perfect square which includes 3 raised to the power 4.

In this example, the prime factors of 1575 are 3, 5, 7. 1575 can be written as a product of all its factors as: \(3^2*5^2*7^1\). So you see, only 7 is having an odd number of powers. if the number gets one more 7, it will can be written as \((3*5*7)^2\), which is a perfect square. Answer is A. 7

If all prime factors are raised to the same even power, then the number is definitely a perfect square. In this example, if 7 is multiplied to 1575, all prime factors become raised to the power 2.

As Bunuel did, I will recommend you to check out the GMAT math book of this forum. To supplement this, you may try out

MGMAT number properties. It covers all such required fundamentals in a very effective way.

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My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html